Shared ground
Paul turns the demand for “proof” back toward the Corinthians themselves (linked to 2 Corinthians 13:3–4). The repeated “test yourselves” is not about curiosity but about a serious evaluation of their real standing “in the faith.” Explicitly, Paul assumes this is something they can assess and “know” about themselves.
Paul also ties this self-recognition to a core Christian claim: “Jesus Christ is in you.” In the flow of the argument, that is presented as what should be true of them if their faith is genuine. He adds a real warning: some may be “unapproved” (failing the test). Finally, Paul expects that an honest assessment of them will also clarify that he and his coworkers are not “unapproved.”
Where interpretation differs (only where needed)
What “in the faith” means. Some read it mainly as holding true belief in the message about Christ; others read it more broadly as continuing loyalty to Christ expressed in the community’s actual life.
What “Christ is in you” means. Some take it as describing Christ’s real indwelling presence in believers; others emphasize it as Christ’s active influence and recognizable alignment with him.
What “unapproved” implies. Some understand it chiefly as being disqualified as genuine Christians; others hear it more as failing the test of authenticity and integrity that would show Christ’s work among them (including how they evaluate Paul).
Why the disagreement exists
The language is relational and diagnostic rather than technical. “Test,” “know,” “in the faith,” and “Christ in you” can refer to inner reality, outward evidence, or both. Also, Paul is arguing in a specific conflict: the Corinthians are assessing Paul, and he redirects attention to what their own condition reveals.
What this passage clearly contributes
These verses explicitly present self-examination as an appropriate response when a community is disputing spiritual credibility. They connect the community’s claimed identity (“in the faith”) with a defining reality (“Christ is in you”), and they treat failure as a genuine possibility (“unless indeed you are unapproved”). The passage also makes a rhetorical link: their verdict on themselves should affect their verdict on Paul’s ministry, since their existence and condition are part of the “evidence.”